
Dataset.  
We use the FIFA 20 player datasethttps://www.kaggle.com/stefanoleone992/fifa-20-complete-player-dataset.
We
predict whether a soccer player's wage is above (\(y=+1\) ) or below (\(y=-1\) ) the median wage based on the player's age and their Overall attribute. For doing so we train a one-hidden-layer NN. We restrict the dataset to contain only players of English or German nationality (leaving us with 2883 players) and consider nationality as sensitive attribute. We train an LSTM [1]} to predict this attribute from a player's name.
In this case we can expect the conditional independence assumption (REF ) to hold since given a player's wage and nationality, their name should be conditionally independent of age and Overall attribute.
Indeed, the measure proposed in [2]}
is small enough (see below) as to confirm that our expectation holds and the independence assumption is satisfied.
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